An equation for a time-dependent profit rate

Taking as a hypothesis a form of the labour theory of value, and $without$ $assuming$ $equilibrium$, we derive an equation that yields the profit-rate $\pi$ as a function of time. For a mature economy, $\pi (t)$ reduces to the product of two factors: ($i$) a certain $retarded$ $average$ of the sum of the growth-rates of productivity and of the size of the labour-force measured by hours worked, and ($ii$) the ratio of the current rate of surplus value to its own retarded average. We also suggest an empirical test of the equation.